I would replace the thermostat, it's a cheap part and could explain the overheating, also is your fan running? If it won;t kick on then there is the overheating prob. Might just be a relay or fuse. You might be blowing fuses because of a short in the heater control pannel. I had to replace it on my 94. It cost about $30 dollars from the junk yard and solved my problems. I would start with these few simple fixes. Hope they help, if not, take it to a garage that offers free estimates, then fix the problems they find. I do that sometimes also. Replace the Thermostat.
Remove the wiring harness from the back of your 2005 Chevy Cavalier heater blower motor. Remove the heater blower motor retaining bolts. Remove the heater blower fan.
Motor hasseized.
You probably have a shorted wire going to the motor or switch. You'll have trace the wires and find the damaged section.
If the heater is blowing the fuse when the blower is turned on, I would suspect the blower motor is defective or locked up. If the A/C is blowing a fuse, suspect a bad clutch, or locked up compressor.
Blown fuse, defective blower motor, or defective blower motor resistor pack.
There might be a bad fuse causing the heater to not work. Check the fuses if they are all ok you may have a bad blower motor. when you turn the heater on and no air is blowing then it is your blower motor.
Heater blower motor is defective and locked up, or possible short in the wiring.
check for a blown fuse that says heater or blower motor
Soot blowing is done in air pre heater by a blower called swing blower which is different from half retractrable or full retractable or deslagger.
check the blower motor resistor
Check the fuses.If not the fuse, test the resistor down by the blower motor.
Blown fuse, defective Blower Motor Resistor Pack, Defective Blower Motor, or Defective Blower Motor speed control switch.